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Hull Number


Let a set of vertices A in a connected graph G be called convex if for every two vertices x,y in A, the vertex set of every (x,y) graph geodesic lies completely in A. Also define the convex hull A subset= V(G) of a graph G with vertex set V(G) as the smallest convex set in G containing A. Then the smallest cardinality of a set A whose convex hull is V(G) is called the hull number of G, denoted h(G).


See also

Geodetic Number

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References

Chartrand, G. and Zhang, P. "The Forcing Hull Number of a Graph." J. Combin. Math. Comb. Comput. 36, 81-94, 2001.Chartrand, G. and Zhang, P. "The Geodetic Number of an Oriented Graph." Europ. J. Combin. 21, 181-189, 2000.Chartrand, G.; Harary, F.; and Zhang, P. "On the Hull Number of a Graph." Ars. Combin. 57, 129-138, 2000.Everett, M. G. and Seidman, S. B. "The Hull Number of a Graph." Discr. Math. 57, 217-223, 1985.Mulder, H. M. "The Expansion Procedure for Graphs." In Contemporary Methods in Graph Theory (Ed. R. Bodendiek). Mannheim, Germany: Wissenschaftsverlag, pp. 459-477, 1990.

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Hull Number

Cite this as:

Weisstein, Eric W. "Hull Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HullNumber.html

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